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a(n) = gcd(binomial(2n,n), 2^n + 1).
1

%I #12 Dec 25 2015 00:04:24

%S 1,1,1,1,3,1,3,1,1,1,3,17,1,5,9,1,3,5,3,1,3,5,3,1,3,1,1,17,3,41,1,1,3,

%T 5,129,1,1,5,1,1,3,5,3,17,9,5,3,1,3,1,9,1,3,5,3,1,3,5,3,17,3,1,3,1,33,

%U 5,3,1,9,115825,3,97,3,5,99,1,129,5,3,1,1,5,3,17,11,5,3,1,3,35425,1,1

%N a(n) = gcd(binomial(2n,n), 2^n + 1).

%H Harry J. Smith, <a href="/A066975/b066975.txt">Table of n, a(n) for n = 1..1000</a>

%t Table[GCD[Binomial[2n,n],2^n+1],{n,100}] (* _Harvey P. Dale_, Aug 26 2012 *)

%o (PARI) { for (n=1, 1000, write("b066975.txt", n, " ", gcd(binomial(2*n, n), 2^n + 1)) ) } \\ _Harry J. Smith_, Apr 12 2010

%K nonn

%O 1,5

%A _Benoit Cloitre_, Jan 26 2002